Review All 3 Systems CW and HW Answer Key

Day 5 CW Algebra 1 Unit 6 Name KEY Solving Systems of Equations Using All Methods WORKSHEET PART 1: SOLVE THE SYSTEM OF EQUATIONS BY GRAPHING 1. y = x + 2 y = 3x - 2 242 y = 2x + 3 y = 2x + 1 3. y = - 3x + 4 y + 3x = - 4 y = - 3x + 4 y = - 3x - 4 PART 2: SOLVE THE SYSTEM OF EQUATIONS BY USING SUBSTITUTION. 4. p = - x - 6 y = x - \mathcal{a} x - 4 = - x - 6 2x - y = - 6 \\ sqrt 4 +4 (2x)/2 = - 2/2 x = - 1 y = - |- 4| = - 5 y = - 5 (-1,-5) 5. y - 3x - 2 x - y - 4 x - (3x - 2) = 4 x - 5x + z = 4 - 2x + 2 = 4 2 - 2 (- 2x)/- 2 = 2/- 2 x = - 1 Y = 3(- 1) - 2 y = - 3 - 2 (- 1, - 5) fi. y = 2x - 10 y = 4x - 8 2x - 10 = 4x - 5 - 10 + 2x - y - 2/2 = (2x)/3 21 - 2x - 3 )=2x+12 - 4x - 6 = 2x + 12 x = - 1 Y = 2(- 1) - 10 y = - 2 + - 10 =-12 (-1,-12) 7. 2y = 2x + 12 y = - 2x - 3 - varphi = varphi*x + 12 \\ -12 aligned -18 b = los log - 3 = x y = - 2(- 3) - 3 y = 6 - 3 = 3 (-3,3) PART 3: SOLVE THE SYSTEM OF EQUATIONS USING ELIMINATION. 8. 4x + 3y = - 5 2(- 2x + 2y = 6) (- 4y - 5)/(x + 4y + 12) y+2 7 (V = 1) 4x + 3(1) = - 5 4x + 3 = - 6 \\ -3-3 aligned (d*varphi*x)/(dx) (-2,1) 9. - 2(8x + 3y = 13) (3x + 2y = 11) - 16x - 16y = - 26y 9x + y = 33 (eta*x)/v = 7/7 3(1) + 2y = 11 3 + 2y = 11 \\ -7 aligned overline Xy lambda = overline x overline x y (1,4) 10. 5y + 4y = - 7 8x - 2y = 1 (yy)/z = - 6/z ( y = - 3 5x + 4(- 3) = - 1 5x-42-1 2 (4x)/5 = 5/5 x - w (1, - 3) 11.2 ! \{- 2x + 2y = 6\} 4y + 2y = - 5 -4412 (4py)/6 = 7/b y = 7/6 q_{1} + 2(7/w) = - 5 4x + 14/1 = - 5 (dx)/h = (- q * q)/(b/u) X = 0/(4pi) - 44/k * L/q = 0/m (- 11/6, 7/6) Day 5 HW Algebra 1-1 DA Name KEY Ch. 5 Applications of Linear Systems Homework Write a system of linear equations for each situation. Solve using substitution or elimination. Make sure that you answer the question. 1. The sum of two numbers is 21. The larger number is 6 less than twice the smaller number. Find the two numbers x + y = 21 y= exists x - b x + 2x - Lx = 21 3x - 4 - 2x 3x = 2 ^ 7 * 1 X = Sma(t) # y= taige a + y = 21; - 9 3. William is 3 years older than Charmaine. The sum of 3 times Charmaine's age and 2 times William's age is 76. How old are William and Charmaine? 11 = 3 + 14 W=17 wewilliam lagege selamine ge W = 3 + C 3c + 2ws = 7Lp 3c + 2(3 + c) = 76 3c + varphi + 2c = 76 5c = 70 (c = 14) 5. Tyshon's age is 3 less than three times Cedric's age. The sum of their ages is 57. How old is Tyshon? Tyshon age T = 3c - 3 C + tau = 57 c + 3c - 3 = 57 C = 6g c - cot x < s - rx T = 3(15) - 3 T = 45 - 3 T = 42 2. The difference of two numbers is 15. The larger number is 1 more than 3 times the smaller number. Find the two numbers. x-small x - y = 15 y = 3x + 1 x - (3x + 1) = 15 x - 3x - 1 = 15 - 2x - 1 = 15 - 2x = 16x Y = 1agc - 7 - y = 15; 45 + 8 - y = 28 y = - 2.3 4. Alysha is two years younger than Bryce. The sum of their ages is 28. How old is Alysha? Alysha age B=Bajce age A = 2 + B A + B = 2B 2 - beta + B = 28 f + 2B =3 overline 8 48/7 = 26/2 B - 1 ^ 2 A = 2 + 13 6. The sum of their ages is 97. The difference of their ages is 19. Find their ages. x + y = 97 x - y = 19 x = 97 - y 77 - y - y = 19 7 - 2y = 1 (- 3y)/- 2 = - 78/- 2 x + 39 = 9 ^ - 1 7. Tickets to the concert were $2.50 for adults and $1 for students. $1200 was collected and 750 tickets were sold. Write a system of linear equations that can be used to find how many adults (a) and how many students (b) attended. How many students attended? System of equations: 2.5x + 1y = 1206 x + y = 750 x = a * du / s * bc*psi + 5 Y= student boket's 2.5x + 750 - x = 1200 1.5x + 750 = 1200 (1.6x)/1.5 = 450/1.5 x = 300 y = 750 - k y = 750 - 360 y = 450 Answer 300 aduh tickets 450 Student tickets